I'm from NZ too, and I have been transferring money from NZ to Chile via an automatic transfer. I'm transferring from my bank account in NZ (ASB) to the bank account of my Chilean partner in Banco de Chile. The first transfer I did from NZ i did manually - go into the bank, fill in forms etc. It took 3 weeks to arrive here in Chile, and then my partner needed to go to the bank to sign for it.
I've since done 3 more transfers, and i've done them all online. They have all taken about 3 days to arrive, and go straight to my partner's account. This past month I transferred more than $US 10,000, although it was in 2 transactions, and didn't have any issues in having the money credited directly.
Unfortunately, it might just be a matter of waiting ....